Problem $3$

Carbon dioxide production from the burning of fossil fuels is a major greenhouse gas and contributor

to global warming. A significant $C{O}_2$ production source is the automotive sector, which through the

combustion of gasoline, generates roughly $1100$ million metric tons of the gas per year. Consider the

potential costs associated with capturing and sequestering this $C{O}_2.$ Let's imagine that we invent a

special device to affix to automobile exhausts that separates all $C{O}_2$ produced so that it can be stored:

In this problem, assume that gasoline can be modeled as n$-$octane and that complete combustion

occurs. Also assume that the temperatures and pressures of all streams in the separator are the same.

The only differences between the streams are their compositions and flowrates. Hint: for this

problem it may help to keep track of numbers and perform calculations using Excel.

$($a$)$ Calculate the standard enthalpy of reaction for n$-$octane combustion, per mol of n$-$octane. You

may need to look up the standard enthalpy of formation of n$-$octane $($gas phase$)$ at the NIST

Chemistry Webbook $($

webbook.nist.gov$)$ or a similar data source.

$($b$)$ Assume that an automobile engine intakes a stream of $6\%$ octane by mass; the remaining mass is

air. Using $1$ mole of fuel $($n$-$octane$)$ as a basis, determine the number of moles of products $C{O}_2,$

$H_{2}O,N_2,$ and $O_2$ after combustion. In turn, calculate the mole fraction of each of these products.

This is the composition of stream $1$ entering the separator. Use a table to report these numbers.

$($c$)$ Assume the separator then removes all of the $C{O}_2$ from the combustion stream $($stream $1),$ leaving

a product $($stream $2)$ of pure $C{O}_2$ and a second product $($stream $3)$ of the remaining gases.

Calculate the number of moles and mole fractions of each of the product streams $2$ and $3$ on

the basis of $1$ mole of fuel.

$($d$)$ Using the expression for the ideal mixing entropy, $S=-R{\displaystyle \underset{?}{\overset{?}{}}}{x}_{i}ln{x}_i$ where $x_i$ is the mole fraction

of species $i,$ calculate the molar entropies $S_1,S_2,S_3$ of each stream in the separator. Then

calculate the total entropies $S_1^t,S_2^t,S_3^t$ of each stream given by the molar entropy times the total

moles in a stream.

$($e$)$ We will consider the most efficient separator. Therefore, apply the second law to the separator

using the open$-$system entropy generation equation in the reversible case. Assume that the

process is at steady state and that the total entropies of each stream are represented by the values

you found in $($d$).$ Calculate the minimum heat flow in $k\frac{J}{m}ol$ fuel $($describing heat that must

be discarded to the environment at $T=298K)$ needed to perform the separation.

$($f$)$ Now apply the open version of the first law to the separator, assuming steady state and that you

can neglect kinetic and potential energy changes. You can also neglect enthalpy changes because

the streams are well$-$described as ideal gases and the process is isothermal. Specifically, calculate

the minimum thermodynamic work $W_S$ in $k\frac{J}{m}ol$ fuel to perform the separation. What

fraction of the enthalpy of combustion does this work cost?

$($g$)$ If fuel costs $$\frac{6}{?}$ gallon, what carbon tax in additional $$/$gallon would be appropriate to cover the

separation costs?